A cylinder has a radius of 5x + 2 and a height of 2x + 8 which polynomial in standard form best describes the total volume of the cylinder? Use the formula V=pi r^2h for the volume of a cylinder. A) 100pi x^4 + 800pi x^3 + 2256pi x^2 + 1408pi x + 256pi B) 50pi x^3 + 240pi x^2 + 168pi x + 32pi C) 20pi x^3 + 168pi x^2 + 384pi x + 128pi D) 10pi x^2 + 44pi x + 16pi

### 5 Answers

B is right: V = pi (2x + 8) (5x + 2)^2 = pi (2x + 8) (25x^2 + 20x + 4) = pi (50x^3 + 40x^2 + 8x + 200x^2 + 160x + 32) = pi (50x^3 + 240x^2 + 168x + 32) = 50pi x^3 + 240pi x^2 + 168pi x + 32pi

This is pretty simple if you take it step by step. So first thing were going to do is suare 5x+2. Remember that you cant just square the 5 and 2 and get your answer. It would by a polynomial. You must do it like this: (5x+2)^2 which is basically (5x+2)(5x+2) So now you foil that and that would give you 25x^2+10x+10x+4 which simplifies to 25x^2+20x+4. Now lets get the height in there as well. (25x^2+20x+4)(2x+8) 50x^3+200x^2+40x^2+160x+8x+32 That simplifies to: 50x^3+240x^2+168x+32 Now when you multiply that to pi that would just multiply each number by pi so: 50pi x^3 + 240pi x^2 + 168 pi x + 32pi So the correct answer would be : Drum roll please:………… B Now you could have just stopped working after you calculated the 50 because there is only one choice with 50 in the answer choices, but it is always good to complete it in case your teacher wants to see all the work. It gets kind of confusing when you simplify because of the x cubed and squared and just x all together so make sure you group them correctly or your answers will be all mixed up, and that won’t look good, especially if there was no multiple choice.

The previous answer is more thorough, but here’s the quick answer. You have to square 5x+2 and multiply that by 2x+8, and then multiply by pi. Look at the first term — you will get 25x^2 * 2x*pi = 50x^3pi. Only B has that term.

Volume of a cylinder is the area of the base times the height. We have the height and a radius, so we can compute the area, then determine the height. A = ÏrÂ² A = Ï(5x + 2)Â² A = Ï(25xÂ² + 20x + 4) Now that we have the area, multiply that by the height to get volume V = Ah V = Ï(25xÂ² + 20x + 4)(2x + 8) V = Ï(50xÂ³ + 200xÂ² + 40xÂ² + 160x + 8x + 32) V = Ï(50xÂ³ + 240xÂ² + 168x + 32) V = 50ÏxÂ³ + 240ÏxÂ² + 168Ïx + 32Ï The answer is B.

What do you not understand? Your set up is there… (5x +2)^2(2x +8)(pi) Do the (5x+2)(5x +2) = __________________ Take above and multiply by (2x +8).

Since you have multiple choice answers, you can multiply the first terms together and get your answer…..